Interference Alignment Solution Research Articles

Interference alignment solution with low complexity based on ring-typed chain design

The future wireless communication network will suffer more serious interference by frequency and spatial reuse. Interference alignment (IA) is an effective transmission strategy to cancel interference, but the closed-form IA solution of low complexity for general interference networks has not been solved well. In this paper, a novel closed-form IA solution method based on improved ring-typed chain design is proposed, for generalized multiple user multiple-input multiple-output (MIMO) interference network. The main idea of this method is to divide each IA transmit matrix into a certain number of sub-matrices, and design elaborately the ring-typed sub-matrix chains to align interfering signal space. Then based on that, the closed-form transmit matrices are derived. Compare with IA solution method proposed in our previous work, this method can achieve more degrees of freedom (DoFs) of each user. Simulation results show the high system sum-rate performance and low computational complexity of the proposed IA solution method.

Interference Alignment Solution with Low Complexity Based on Ring-Typed Chain Design}

Interference Alignment Solution with Low Complexity Based on Ring-Typed Chain Design}

Alignment Chain-Based Closed-Form IA Solution for Multiple User MIMO Interference Networks

As a potential interference management technique, interference alignment (IA) can enormously improve the system capacity in the future mobile communication networks. However, the general closed-form IA solution in the multiple user scenario is still an open problem, which hinders the implementation due to the high complexity of iterative IA design. In this paper, a alignment chain-based closed-form IA solution scheme is proposed for generalized $K (K > 3)$ -user multiple-input multiple-output (MIMO) interference channel. The alignment chains are sophisticatedly designed, on the basis of compressing the interference subspace and improving the degree of freedom (DoF) as much as possible. Then based on the alignment chains, the alignment chain equations are built, and the least-squares IA solution with optimal DoF or the exact IA solution with reduced DoF is provided, by using the theory of matrices. A series of simulation experiments are carried out to verify the proposed closed-form IA solution, and simulation results demonstrate its effectiveness and low computational complexity.

Cyclic Interference Alignment for Full-Duplex Multi-Antenna Cellular Networks

This paper studies full-duplex (FD) cellular networks in which a base station (BS) operated in FD mode with multiple antennas supports multiple uplink and downlink users simultaneously in the same wireless channel. Two typical FD cellular scenarios are considered, one with half-duplex (HD) users and the other with FD users along with the FD BS. For both the cases, a novel constructive method is developed for finding a closed-form interference alignment (IA) solution, named cyclic IA . The core idea behind this approach is to construct a set of loop-equations enabling IA in a cyclic manner, so that beamforming vectors are sequentially determined by solving an eigenvalue problem. It is shown analytically that the proposed cyclic IA can achieve the optimal sum degrees-of-freedom (DoF) when the number of user antennas is large enough to meet the derived conditions. In particular, it is shown that the proposed scheme achieves a twofold DoF gain compared with conventional HD cellular networks even in the presence of inter-link interference, provided the number of users becomes large enough compared with the ratio of the number of BSs and user antennas. Simulation results demonstrate that not only are the analytical DoF results valid, but under a practical multi-cell scenario, the proposed cyclic IA offers significant throughput gains depending on the cell radius.

Homotopy Continuation for Spatial Interference Alignment in Arbitrary MIMO X Networks

In this paper, we propose an algorithm to design interference alignment (IA) precoding and decoding matrices for arbitrary MIMO X networks. The proposed algorithm is rooted in the homotopy continuation techniques commonly used to solve systems of nonlinear equations. Homotopy methods find the solution of a target system by smoothly deforming the solution of a start system which can be trivially solved. Unlike previously proposed IA algorithms, the homotopy continuation technique allows us to solve the IA problem for both unstructured (i.e., generic) and structured channels such as those that arise when time or frequency symbol extensions are jointly employed with the spatial dimension. To this end, we consider an extended system of bilinear equations that include the standard alignment equations to cancel the interference, and a new set of bilinear equations that preserve the desired dimensionality of the signal spaces at the intended receivers. We propose a simple method to obtain the start system by randomly choosing a set of precoders and decoders, and then finding a set of channels satisfying the system equations, which is a linear problem. Once the start system is available, standard prediction and correction techniques are applied to track the solution all the way to the target system. We analyze the convergence of the proposed algorithm and prove that, for many feasible systems and a sufficiently small continuation parameter, the algorithm converges with probability one to a perfect IA solution. The simulation results show that the proposed algorithm is able to consistently find solutions achieving the maximum number of degrees of freedom in a variety of MIMO X networks with or without symbol extensions. Further, the algorithm provides insights into the feasibility of IA in MIMO X networks for which theoretical results are scarce.

Low Complexity Interference Alignment for mmWave MIMO Channels in Three-Cell Mobile Network

Millimeter wave (mmWave) communications are an important candidate technique in 5G networks for features, supporting ultra-dense small cells and mobile data offloading. However, ultra-dense nodes and increasing data traffic bring in vast interference. This paper investigates low complexity non-iterative interference alignment (IA) schemes for multiple-input multiple-output (MIMO) interference broadcast channels in mmWave communications. The authors focus on the three-cell mobile network model in which each base station supports no more than two users within its cell. There is already a closed-form IA solution for the case that one cell has two users, while the other two have one user in each, which can be denoted as {2,1,1}. This paper considers different settings and proposes corresponding IA schemes. First, two IA schemes based on multi-step for the asymmetric setting {2,2,1} are presented, five degree of freedom (DoF) could be achieved. Then, for the symmetric setting {2,2,2}, a novel IA solution with lower complexity and a joint method combining IA with non-iterative multi-user MIMO technique are proposed, and they can achieve six DoF. The simulation results indicate that our non-iterative schemes have similar sum-rate capacity performances with the iterative ones in existing work, and the complexity is effectively reduced.

Role of Interference Alignment in Wireless Cellular Network Optimization

The emergence of interference alignment (IA) as a degrees-of-freedom optimal strategy motivates the need to investigate whether IA can be leveraged to aid conventional network utility maximization algorithms, which are typically only capable of finding locally optimal solutions. To test the usefulness of IA in this context, this paper proposes a two-stage optimization framework for the downlink of a $G$ -cell multi-antenna network with $K$ users/cell. The first stage of the proposed framework focuses on nulling interference from a set of dominant interferers using IA, while the second stage optimizes transmit and receive beamformers to maximize a network-wide utility using the IA solution as the initial condition. Further, this paper establishes a set of new feasibility results for partial IA that can be used to guide the number of dominant interferers to be nulled in the first stage. Through simulations on specific topologies of a cluster of base stations, it is observed that the impact of IA depends on the choice of the utility function and the presence of out-of-cluster interference. In the absence of out-of-cluster interference, the proposed framework outperforms straightforward optimization when maximizing the minimum rate, while providing marginal gains when maximizing sum rate. However, the benefit of IA is greatly diminished in the presence of significant out-of-cluster interference.

Near‐optimal practical convergent method for interference alignment in MIMO interference channels

A practical distributed Gauss–Newton method for the near-optimal computation of interference alignment solutions is proposed, based on the block-wise structure of Jacobian matrix of the residual interference function. Also, a simple practical matrix inverse computation algorithm to solve the rank-deficient problem due to the interference sparse matrix is adopted. This proposal achieves convergent performance comparable to centralised Gauss–Newton method, with the major advantage of being practically implemented in a distributed manner.

On the Number of Interference Alignment Solutions for the $K$ -User MIMO Channel With Constant Coefficients

In this paper, we study the number of different interference alignment (IA) solutions in a $K$ -user multiple-input multiple-output (MIMO) interference channel, when the alignment is performed via beamforming and no symbol extensions are allowed. We focus on the case where the number of IA equations matches the number of variables. In this situation, the number of IA solutions is finite and constant for any channel realization out of a zero-measure set and, as we prove in this paper, it is given by an integral formula that can be numerically approximated using Monte Carlo integration methods. More precisely, the number of alignment solutions is the scaled average of the determinant of a certain Hermitian matrix related to the geometry of the problem. Interestingly, while the value of this determinant at an arbitrary point can be used to check the feasibility of the IA problem, its average (properly scaled) gives the number of solutions. For single-beam systems, the asymptotic growth rate of the number of solutions is analyzed and some connections with classical combinatorial problems are presented. Nonetheless, our results can be applied to arbitrary interference MIMO networks, with any number of users, antennas, and streams per user.

A Quadratically Convergent Method for Interference Alignment in MIMO Interference Channels

Alternating minimization and steepest descent are commonly used strategies to obtain interference alignment (IA) solutions in the -user multiple-input multiple-output (MIMO) interference channel (IC). Although these algorithms are shown to converge monotonically, they experience a poor convergence rate, requiring an enormous amount of iterations which substantially increases with the size of the scenario. To alleviate this drawback, in this letter we resort to the Gauss-Newton (GN) method, which is well-known to experience quadratic convergence when the iterates are sufficiently close to the optimum. We discuss the con- vergence properties of the proposed GN algorithm and provide several numerical examples showing that it always converges to the optimum with quadratic rate, reducing dramatically the required computation time in comparison to other algorithms, hence paving a new way for the design of IA algorithms.

Vidyut

Global synchronization across time and frequency domains significantly benefits wireless communications. Multi-Cell (Network) MIMO, interference alignment solutions, opportunistic routing techniques in ad-hoc networks, OFDMA etc. all necessitate synchronization in either time or frequency domain or both. This paper presents sysname, a system that exploits the easily accessible and ubiquitous power line infrastructure to achieve synchronization in time and frequency domains across nodes distributed beyond a single-collision domain. sysname uses the power lines to transmit a reference frequency tone to which each node locks its frequency. sysname exploits the steady periodicity of delivered power signal itself to synchronize distributed nodes in time. We validate the extent of sysname's synchronization and evaluate its effectiveness. We verify sysname's suitability for wireless applications such as OFDMA and multi-cell MIMO by validating the benefits of global synchronization in an enterprise wireless network. Our experiments show a throughput gain of 8.2x over MegaMIMO, 7x over NemoX and 2.5x over OFDMA systems. Enterprise wireless networks are supported by an Ethernet backbone. Researchers have been exploring techniques over the backbone to enable and assist in improving the performance of the wireless networks. Recent work also showed the benefit of sharing information in the air between the nodes to enable higher performance of the network. Even sharing information as little as synchronization information has been demonstrated to open new avenues (such as MU-MIMO, Physical Network Coding, Opportunistic routing, etc.) for the wireless networks to enhance its performance. However, another medium shared by majority of the nodes in the enterprise network - the power line infrastructure - has been largely left untapped to assist the wireless network. While the power lines are noisy and have a frequency selective transmission characteristic, its uniqueness is that its range can extend beyond that over air while it is unburdened by switching and other responsibilities of the Ethernet backbone. This paper poses the following question: How best to exploit the opportunity presented by the power lines to further enhance enterprise wireless networks? The key contributions of this paper are the following: Identify and demonstrate the feasibility of utilizing power lines as a medium to achieve synchronization (in time and frequency domains) between nodes in the network; Demonstrate the scalability of this technique by achieving synchronization between nodes beyond the transmission range of any of the individual nodes. The paper presents empirical results pertaining to the accuracy of synchronization and the benefit of the proposed synchronization method to existing distributed wireless techniques by virtue of extension across multiple collision domains.

A Leakage-Based Solution for Interference Alignment in MIMO Interference Channel Networks

Most recent research on iterative solutions for interference alignment (IA) presents solutions assuming channel reciprocity based on the suppression of interference from undesired sources by using an appropriate decoding matrix also known as a receiver combining matrix for multiple input multiple output (MIMO) interference channel networks and reciprocal networks. In this paper, we present an alternative solution for IA by designing precoding and decoding matrices based on the concept of signal leakage (the measure of signal power that leaks to unintended users) on each transmit side. We propose an iterative algorithm for an IA solution based on maximization of the signal-to-leakage-and-noise ratio (SLNR) of the transmitted signal from each transmitter. In order to make an algorithm removing the requirement of channel reciprocity, we deploy maximization of the signal-to-interference-and-noise ratio (SINR) in the design of the decoding matrices. We show through simulation that minimizing the leakage in each transmission can help achieve enhanced performance in terms of aggregate sum capacity in the system.

A Closed-Form Solution to Implement Interference Alignment and Cancellation for a Gaussian Interference Multiple Access Channel

For interference alignment (IA) with no channel extension, determining the existence of IA solution for general system parameters is still an open problem. This same problem also exists in interference alignment and cancellation (IAC), which combines IA with interference cancellation in the receivers, involving a new receiver architecture associated with signaling over backhaul links among them. As IAC is expected to achieve more degrees of freedom (DoF) than IA, the existence of IAC solution would be another interesting, yet challenging issue to investigate. In this paper, we have proposed a specific alignment scheme, which allows for the derivation of closed-form IAC solution. Furthermore, we establish and prove the general necessary and sufficient condition to determine the existence of closed-form IAC solution for a Gaussian interference multiple access channel (MAC) with K receivers and J users, each with M antennas.

Pair-Aware Interference Alignment in Multi-User Two-Way Relay Networks

In this paper, K bidirectionally communicating node pairs with each node having N antennas and one amplify and forward relay having R antennas are considered. Each node wants to transmit d data streams to its communication partner. Taking into account that each node can perform self interference cancellation, a new scheme called Pair-Aware Interference Alignment is proposed. In this scheme, the transmit precoding matrices and the relay processing matrix are chosen in such a way that at any given receiver all the interfering signals except the self interference are within the interference subspace and the useful signal is in a subspace linearly independent of the interference subspace. If the number of variables is larger than or equal to the number of constraints in the system, the system is classified as proper, else as improper. Through simulations it is shown that for a proper system (2Kd≤2N+R-d), interferences can be perfectly aligned and the useful signals can be decoded interference-free at the receivers. An iterative algorithm to achieve the interference alignment solution is proposed. Also for the proper system fulfilling a certain additional condition, which will be derived in this paper, a closed form solution is proposed.

On the Achievability of Interference Alignment for Three-Cell Constant Cellular Interfering Networks

For a three-cell constant cellular interfering network, a new property of alignment is identified, i.e., an interference alignment (IA) solution obtained in a user-cooperation scenario can also be applied to a non-cooperation environment. By using this property, an algorithm is proposed by jointly designing transmit and receive beamforming matrices. Analysis and simulation results show that more degrees of freedom (DoF) can be achieved compared with conventional schemes in most cases.

Low complexity interference alignment algorithms for desired signal power maximization problem of MIMO channels

In this article, we investigate the interference alignment (IA) solution for a K-user MIMO interference channel. Proper users’ precoders and decoders are designed through a desired signal power maximization model with IA conditions as constraints, which forms a complex matrix optimization problem. We propose two low complexity algorithms, both of which apply the Courant penalty function technique to combine the leakage interference and the desired signal power together as the new objective function. The first proposed algorithm is the modified alternating minimization algorithm (MAMA), where each subproblem has closed-form solution with an eigenvalue decomposition. To further reduce algorithm complexity, we propose a hybrid algorithm which consists of two parts. As the first part, the algorithm iterates with Householder transformation to preserve the orthogonality of precoders and decoders. In each iteration, the matrix optimization problem is considered in a sequence of 2D subspaces, which leads to one dimensional optimization subproblems. From any initial point, this algorithm obtains precoders and decoders with low leakage interference in short time. In the second part, to exploit the advantage of MAMA, it continues to iterate to perfectly align the interference from the output point of the first part. Analysis shows that in one iteration generally both proposed two algorithms have lower computational complexity than the existed maximum signal power (MSP) algorithm, and the hybrid algorithm enjoys lower complexity than MAMA. Simulations reveal that both proposed algorithms achieve similar performances as the MSP algorithm with less executing time, and show better performances than the existed alternating minimization algorithm in terms of sum rate. Besides, from the view of convergence rate, simulation results show that the MAMA enjoys fastest speed with respect to a certain sum rate value, while hybrid algorithm converges fastest to eliminate interference.

Feasibility Condition for Interference Alignment With Diversity

This paper studies the diversity benefit of different interference alignment solutions. While most research about interference alignment was aiming at deriving or realizing the maximum achievable multiplexing gain, the symbol error rate performance, which can be characterized by the diversity gain is of equal importance. Different interference alignment solutions are classified into two categories called diversity interference alignment and zero-forcing interference alignment. Although these two types of solutions are not distinguishable in terms of the multiplexing gain, this paper will show their difference lies in the fact that they have different diversity gains. In this paper, a K-user (M × N) interference channel is used, with each user sending 1 degree of freedom of information by using interference alignment precoding and receiving filters but without space-time codes. The feasibility conditions for diversity interference alignment to be achieved are analyzed and the diversity orders different solutions can provide are compared. The results imply that diversity interference alignment solutions offer both multiplexing and diversity gains simultaneously. It also tells us two important rules about the interference alignment precoding filters design: an optimal design has to take both desired and interference channel matrices into consideration and the separation of interference alignment precoding filters design and space-time codes design may not be optimal in general.

On Feasibility of Interference Alignment in MIMO Interference Networks

The degrees of freedom of MIMO interference networks with constant channel coefficients are not known in general. Determining the feasibility of a linear interference alignment solution is a key step toward solving this open problem. Our approach in this paper is to view the alignment problem as a system of bilinear equations and determine its solvability by comparing the number of equations and the number of variables. To this end, we divide interference alignment problems into two classes - proper and improper. An interference alignment problem is called proper if the number of equations does not exceed the number of variables. Otherwise, it is called improper. Examples are presented to support the intuition that for generic channel matrices, proper systems are almost surely feasible and improper systems are almost surely infeasible.